Common Mistakes

Frequent Errors

1. Saying $f(x+h)$ shifts right when $h>0$ (it shifts left). 2. Saying $f(bx)$ stretches by $b$ horizontally (factor is $1/|b|$). 3. Ignoring $x$-axis reflection when $a<0$. 4. Ignoring $y$-axis reflection when $b<0$. 5. Applying vertical and horizontal moves to the wrong coordinate of a point. 6. Forgetting order when combining (horizontal inside affects $x$ first conceptually). 7. Keeping the parent domain after shifting $\sqrt{x}$ or $1/x$. 8. Writing the equation with $h$ sign flipped relative to the verbal “right/left.”

Why These Happen

Horizontal changes feel “backwards,” and stretch/compress language is easy to swap between $x$ and $y$. Negative coefficients get treated as plain size changes.

How to Fix Them

• Script: “$f(x-4)$ replaces $x$ with $x-4$ → need larger $x$ → right 4.”
• Table: transformation | effect on $x$ | effect on $y$.
• Always map one concrete point.
• Recompute domain from the final formula.

Avoidance Scripts

• “Inside with $+h$ moves left by $h$.”
• “Horizontal scale factor is $1/|b|$. ”
• “Negative $a$ or $b$ means a reflection.”

Quick Self-Check

• Did I get horizontal direction right?
• Did I use $1/|b|$ for $f(bx)$?
• Did I mention reflections?
• Did domain/range change?